Posted by John Swensen on February 17, 2000 at 14:51:08:
In Reply to: Re: CC fingering chart posted by Sean Chisham on February 16, 2000 at 21:44:31:
I wrote a simple program to calculate the errors of various valve combinations when used to lower an open note by up to 11 half-steps. For this example, the fifth valve is a flat-whole step, defined to lower the pitch by a perfect fifth, when used with the fourth valve (eg. a low F on a CC tuba, low Eb on a BBb, low Bb on an F, etc.).
Because the open notes may not be exactly in tune, the best tuning of a note may not have have the lowest error; the relative tuning of other fingerings is shown to aid in selecting a better fingering. I didn't bother listing fingerings with more than 50 cents error.
slide 1 = 200.00 cents (whole step)
slide 2 = 100.00 cents (half step)
slide 3 = 300.00 cents (minor third, larger than 12)
slide 4 = 500.00 cents (perfect fourth)
slide 5 = 262.12 cents (flat whole step---perfect fifth with 4)
0 half steps:
0: 0.0 cents sharp
1 half steps:
2: 0.0 cents sharp
2 half steps:
1: 0.0 cents sharp
3 half steps:
12: 10.6 cents sharp
3: 0.0 cents sharp
5: 37.9 cents sharp
25: 48.4 cents flat
4 half steps:
23: 15.5 cents sharp
15: 35.4 cents flat
5 half steps:
13: 30.3 cents sharp
123: 46.4 cents flat
4: 0.0 cents sharp
125: 13.6 cents flat
35: 23.0 cents flat
6 half steps:
24: 24.5 cents sharp
235: 2.5 cents sharp
7 half steps:
14: 48.0 cents sharp
124: 21.2 cents flat
34: 29.5 cents flat
135: 27.0 cents sharp
1235: 41.4 cents flat
45: 0.0 cents sharp
8 half steps:
234: 4.2 cents sharp
145: 36.0 cents flat
245: 32.6 cents sharp
9 half steps:
134: 36.7 cents sharp
1234: 24.7 cents flat
1245: 1.6 cents sharp
345: 5.9 cents flat
10 half steps:
1345: 27.2 cents flat
2345: 34.2 cents sharp
11 half steps:
12345: 16.9 cents sharp